Finite-Dimensional PT-Symmetric Hamiltonians |
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Authors: | Qinghai Wang |
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Institution: | (1) Department of Physics, Washington University, St. Louis, MO 63130, USA |
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Abstract: | This paper investigates finite-dimensional PT-symmetric Hamiltonians. It is shown here that there are two ways to extend real symmetric Hamiltonians into the complex domain: (i) The usual approach is to generalize such Hamiltonians to include complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the first approach the spectrum remains real, while in the second approach the spectrum remains real if the PT symmetry is not broken. Both generalizations give a consistent theory of quantum mechanics, but if D>2, a D-dimensional Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional PT-symmetric matrix Hamiltonian. |
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Keywords: | PT symmetry non-Hermitian Hamiltonian matrix |
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